Semileptonic decays of doubly charmed or bottom baryons to single heavy baryons

TL;DR

This work investigates semileptonic decays of doubly charmed and doubly bottom baryons to single heavy baryons using a three-point QCD sum-rule approach, incorporating nonperturbative operators up to mass dimension five. Form factors for the $B\to B'$ transitions are extracted from a physical (hadronic) side and a QCD (OPE) side via a double Borel transform, with interpolating currents for the initial and final baryons and a transition current. The six form factors $F_1$, $F_2$, $F_3$, $G_1$, $G_2$, $G_3$ are computed across $q^2$ and fitted with a rational function, enabling predictions of decay widths and branching ratios across all lepton channels, including $e$, $\mu$, and $\tau$. The results, anchored by updated masses and residues for doubly heavy baryons, provide concrete benchmarks for upcoming measurements at LHCb and offer insight into the weak decay mechanisms of these exotic states. Overall, the paper contributes a comprehensive, QCD-grounded set of predictions for doubly heavy baryon semileptonic decays that can be tested experimentally and refined with future data.

Abstract

We investigate the semileptonic decays of baryons containing double charm or double bottom quarks, focusing on their transitions to single heavy baryons through three-point QCD sum rule framework. In our calculations, we take into account nonperturbative operators with mass dimensions up to five. We calculate the form factors associated with these decays, emphasizing the vector and axial-vector transition currents in the corresponding amplitude. By applying fitting functions for the form factors based on the squared momentum transfer, we derive predictions for decay widths and branching ratios in their possible lepton channels. These findings offer valuable insights for experimentalists exploring semileptonic decays of doubly charm or bottom baryons. Perhaps they can be validated in upcoming experiments like LHCb. These investigations contribute to a deeper understanding of the decay mechanisms in these baryonic channels.

Figures (11)

• Figure 1: Doubly charm baryons with spin-$1/2$. The case is similar for the doubly bottom baryons and those containing bottom and charm quarks.
• Figure 2: Antitriplets (Panel a) and Sextets (Panel b) of single charm baryons featuring one charm quark and two light quarks. The pattern is similar for the baryons containing a bottom quark. These baryons have a total spin of 1/2, while other sextet exhibiting spin 3/2 are not shown in the figure.
• Figure 3: Feynman diagram depicting the decay of doubly heavy baryons $B$ into a single heavy baryons $B^{\prime}$, with two spectator quarks forming a diquark. The momentum of the initial and final baryons are represented as $p$ and $p^{\prime}$ respectively. At the quark level, a heavy quark $Q_{1}$ transits into a light quark $q_{1}$, and we have two spectator quarks. The black circle symbolizes the weak interaction vertex.
• Figure 4: Form factors of $\Omega_{bb}^{-}\rightarrow \Xi^0_{b} {\ell} \bar{\nu_{\ell}}$, as an example, as a function of the Borel parameter $M^2$ for variuos $s_0$ amounts, with $q^2=0$ and other auxiliary parameters set to their central values. The graphs represent the structures $\slashed{p}'\gamma_{\mu}$, $p_{\mu}\slashed{p'}\slashed{p}$, $p'_{\mu}\slashed{p'}\slashed{p}$, $\gamma_{\mu} \gamma_5$, $p_{\mu}\slashed{p}'\slashed{p}\gamma_5$, and $p'_{\mu}\gamma_5$ corresponding to $F_1$, $F_2$, $F_3$, $G_1$, $G_2$, and $G_3$, respectively.
• Figure 5: Form factors of $\Omega_{bb}^{-}\rightarrow \Xi^0_{b} {\ell} \bar{\nu_{\ell}}$, as an example, as a function of the Borel parameter $M'^2$ for variuos $s'_0$ amounts, with $q^2=0$ and other auxiliary parameters set to their central values. The graphs represent the structures $\slashed{p}'\gamma_{\mu}$, $p_{\mu}\slashed{p'}\slashed{p}$, $p'_{\mu}\slashed{p'}\slashed{p}$, $\gamma_{\mu} \gamma_5$, $p_{\mu}\slashed{p}'\slashed{p}\gamma_5$, and $p'_{\mu}\gamma_5$ corresponding to $F_1$, $F_2$, $F_3$, $G_1$, $G_2$, and $G_3$, respectively.